U.S. patent application number 12/424957 was filed with the patent office on 2010-10-21 for tampering detection system using quantum-mechanical systems.
Invention is credited to Ryan S. Bennink, Warren P. Grice, Travis S. Humble.
Application Number | 20100265077 12/424957 |
Document ID | / |
Family ID | 42980598 |
Filed Date | 2010-10-21 |
United States Patent
Application |
20100265077 |
Kind Code |
A1 |
Humble; Travis S. ; et
al. |
October 21, 2010 |
Tampering Detection System Using Quantum-Mechanical Systems
Abstract
The use of quantum-mechanically entangled photons for monitoring
the integrity of a physical border or a communication link is
described. The no-cloning principle of quantum information science
is used as protection against an intruder's ability to spoof a
sensor receiver using a `classical` intercept-resend attack.
Correlated measurement outcomes from polarization-entangled photons
are used to protect against quantum intercept-resend attacks, i.e.,
attacks using quantum teleportation.
Inventors: |
Humble; Travis S.;
(Knoxville, TN) ; Bennink; Ryan S.; (Knoxville,
TN) ; Grice; Warren P.; (Oak Ridge, TN) |
Correspondence
Address: |
ORNL-UTB-LUEDEKA, NEELY & GRAHAM
P.O. BOX 1871
KNOXVILLE
TN
37901
US
|
Family ID: |
42980598 |
Appl. No.: |
12/424957 |
Filed: |
April 16, 2009 |
Current U.S.
Class: |
340/600 |
Current CPC
Class: |
G08B 13/124 20130101;
G08B 13/186 20130101 |
Class at
Publication: |
340/600 |
International
Class: |
G08B 17/12 20060101
G08B017/12 |
Goverment Interests
GOVERNMENT RIGHTS
[0001] This invention was made with government support under
Contract No. DE-AC05-00OR22725 awarded by the U.S. Department of
Energy. The government has certain rights in the invention.
Claims
1. A system for monitoring the integrity of a boundary comprising:
a source apparatus for generating a first and a second quantum
system, the first and the second quantum systems being quantum
mechanically entangled in at least one monitored physical property;
a transmission medium disposed adjacent the boundary; a first
receiver and a second receiver; a transmission apparatus for
directing the first quantum system through the transmission medium
to the first receiver and for directing the second quantum system
to the second receiver; an evaluation apparatus for assessing a
first verifying quantum system received by the first receiver and
for assessing a second verifying quantum system received by the
second receiver and for estimating whether the first verifying
quantum system and the second verifying quantum system are quantum
mechanically entangled in the at least one monitored physical
property; and an alarm apparatus for indicating a possible
compromise of the boundary if the first verifying quantum system
and the second verifying quantum system are not likely quantum
mechanically entangled in the at least one monitored physical
property.
2. The system of claim 1 wherein the source apparatus comprises a
spontaneous parametric down conversion photon pair generator and
the first and the second quantum system comprise a pair of quantum
mechanically entangled photons.
3. The system of claim 1 wherein the at least one monitored
physical property comprises an entangled polarization
characteristic of the first and the second quantum systems.
4. The system of claim 1 wherein the at least one monitored
physical property comprises an entangled frequency characteristic
of the first and second quantum systems.
5. The system of claim 1 wherein the at least one monitored
physical property comprises an entangled polarization
characteristic and an entangled frequency characteristic of the
first and the second quantum systems.
6. The system of claim 1 wherein the transmission medium comprises
the atmosphere.
7. The system of claim 1 wherein the transmission medium comprises
a fiber optic cable.
8. A system for monitoring the integrity of a communication link
comprising: a source apparatus for generating a first and a second
quantum system, the first and the second quantum systems being
quantum mechanically entangled in at least one monitored physical
property, with each monitored physical property having a value pair
corresponding to the first and the second quantum system; a first
receiver and a second receiver; a transmission apparatus for
directing the first quantum system through the communication link
to the first receiver and for directing the second quantum system
to the second receiver; a first evaluation apparatus for estimating
a first value of each monitored physical property of a first
verifying quantum system received by the first receiver; a second
evaluation apparatus for estimating a second value of each
monitored physical property of a second verifying quantum system
received by the second receiver; and an alarm system for indicating
a possible compromise of the communication link if the estimated
first value of each monitored physical property of the first
verifying quantum system and the estimated second value of each
monitored physical property of the second verifying quantum system
are not likely equal to the paired values of each monitored
physical property.
9. The system of claim 8 wherein the source apparatus comprises a
spontaneous parametric down conversion photon pair generator and
the first and the second quantum system comprises a pair of
photons.
10. The system of claim 8 wherein the first and the second quantum
system comprise a polarization-entangled photon pair and the at
least one monitored physical property and value pair comprises a
monitored physical property with a value pair selected from the
group consisting of (a) h/v polarization with a value pair of
(0.degree.,90.degree.), (b) diagonal/anti-diagonal polarization
with a value pair of (+45.degree.,-45.degree.), and (c) circular
polarization with a value pair of (right, left).
11. The system of claim 8 wherein the at least one monitored
physical property comprises an entangled frequency characteristic
of the first and second quantum systems.
12. The system of claim 8 wherein the at least one monitored
physical property comprises an entangled polarization
characteristic and an entangled frequency characteristic of the
first and second quantum systems.
13. The system of claim 8 wherein the transmission medium comprises
the atmosphere.
14. The system of claim 8 wherein the transmission medium comprises
a fiber optic cable.
15. A system for monitoring the integrity of a transmission of a
quantum system comprising: an apparatus for generating the quantum
system with an as-transmitted value of a monitored physical
property; a transmission medium; a receiver; a transmission
apparatus for directing the quantum system through the transmission
medium to the receiver; an evaluation system for estimating an
as-received value of the monitored physical property of a verifying
quantum system received by the receiver; and an alarm system for
comparing the as-transmitted value of the monitored physical
property of the transmitted quantum system with the as-received
value of the monitored physical property of the verifying quantum
system and for indicating a possible compromise of the transmission
of the quantum system if the estimated as-received value of the
monitored physical property of the verifying quantum system does
not likely correspond to the as-transmitted value of the monitored
physical property of the transmitted quantum system.
16. The system of claim 15 wherein the monitored physical property
comprises a polarization characteristic of the quantum system.
17. The system of claim 15 wherein the transmission medium
comprises the atmosphere.
18. The system of claim 15 wherein the transmission medium
comprises a fiber optic cable.
19. A method for monitoring the integrity of a boundary comprising:
generating a first and a second quantum system, the first and the
second quantum systems being quantum mechanically entangled in at
least one monitored physical property; transmitting the first
quantum system through a transmission medium along the boundary to
a first receiver and transmitting the second quantum system to a
second receiver; estimating whether the first verifying quantum
system received by the first receiver and the second verifying
quantum system received by the second receiver are quantum
mechanically entangled in the at least one monitored physical
property; and generating an indication of possible compromise of
the boundary if the first verifying quantum system and the second
verifying quantum system are not likely quantum mechanically
entangled in the at least one monitored physical property.
20. A method for monitoring the integrity of a communication link
comprising: generating a first and a second quantum system, the
first and the second quantum systems being quantum mechanically
entangled in at least one monitored physical property, with each
monitored physical property having a value pair corresponding to
the first and the second quantum system; transmitting the first
quantum system through the communication link to a first receiver
and transmitting the second quantum system to a second receiver;
estimating a first value of each monitored physical property of a
first verifying quantum system received by the first receiver;
estimating a second value of each monitored physical property of a
second verifying quantum system received by the second receiver;
comparing the estimated first value of each monitored physical
property of the first verifying quantum system with the estimated
second value of each monitored physical property of the second
verifying quantum system; and generating an indication of a
possible compromise of the communication link if the estimated
first value of each monitored physical property of the first
verifying quantum system and the estimated second value of each
monitored physical property of the second verifying quantum system
are not likely equal to the value pair of each monitored physical
property.
21. A method for monitoring the integrity of a transmission of a
quantum system comprising: generating the quantum system with an
as-transmitted value of a monitored physical property; transmitting
the quantum system through a transmission medium to a receiver;
estimating an as-received value of the monitored physical property
of a verifying quantum system received by the receiver; comparing
the as-transmitted value of the monitored physical property of the
transmitted quantum system with the estimated as-received value of
the monitored physical property of the verifying quantum system;
and indicating a possible compromise of the transmission of the
quantum system if the estimated as-received value of the monitored
physical property of the verifying quantum system does not likely
correspond to the as-transmitted value of the monitored physical
property of the transmitted quantum system.
22. A method for verifying the integrity of a physical perimeter
comprising the steps of: generating an entangled pair of first and
second quantum systems; directing the first quantum system about
the physical perimeter; and comparing the first quantum system with
the second quantum system for verification of the authenticity of
the first quantum system.
23. The method of claim 22 wherein the first and the second quantum
systems comprise a photon pair.
24. The method of claim 22 further comprising a step of generating
an alert if the authenticity of the first quantum system is not
verified.
Description
FIELD
[0002] This disclosure relates to the field of security systems.
More particularly, this disclosure relates to detection of
tampering with security systems.
BACKGROUND
[0003] Many government, industrial, and commercial entities have a
need to protect various aspects of their endeavors from hostile
physical intrusion. Such intrusions may range from terrorist
attacks to burglary attempts to mischievous mayhem to industrial or
military espionage. To prevent such actions it is often desirable
to secure the property boundaries at sensitive sites such as
nuclear and chemical facilities, military bases, and other
sensitive installations. Sometimes such protection focuses on a
boundary of a particular facility such as a warehouse, a vault, a
storage crib, or a similar protected zone. In some instances a
security system may be employed to monitor a physical boundary
associated with such a system. For example, a fence around a
protected property may include an electronic continuity circuit
that is designed to detect a break in the fence that could indicate
an intrusion into the property. In some instances a security system
may be employed to monitor the physical integrity of a secured
space. Examples of such security systems are window and door
alarms, motion detectors, and optical beam interruption detectors.
Also, distribution systems such as gas and oil pipelines,
electrical distribution systems, and voice and data communication
lines often warrant special security measures. In the case of
pipelines, fluid pressure monitors may be used to detection
intrusion of the boundary (i.e., the path) of a pipeline. In the
case of electrical power distribution systems and communication
systems, the detection of service interruption may be used to
detect tampering with the "boundary" (i.e., the
distribution/communication lines) associated with such systems.
However in the case of communication lines it is often necessary to
also protect against eavesdropping, and various detection systems
have been developed for that purpose. However adversary nations,
terrorists, rogue organizations, and thieves are becoming
increasingly technically sophisticated in their abilities to attack
and thwart such security measures. What are needed therefore are
improved security systems for protecting various boundaries and
communication lines from compromise by such attacks.
SUMMARY
[0004] In one embodiment the present disclosure provides a system
for monitoring the integrity of a boundary. The system includes a
source apparatus for generating a first and a second quantum
system, where the first and the second quantum systems are quantum
mechanically entangled in at least one monitored physical property.
There is a transmission medium disposed along the boundary. A first
receiver and a second receiver are provided. There is a
transmission apparatus that is provided for directing the first
quantum system through the transmission medium to the first
receiver and for directing the second quantum system to the second
receiver. There is an evaluation apparatus that is provided for
assessing a first verifying quantum system received by the first
receiver and for assessing a second verifying quantum system
received by the second receiver. The evaluation apparatus also
estimates whether the first verifying quantum system and the second
verifying quantum system are quantum mechanically entangled in the
at least one monitored physical property. Further provided is an
alarm apparatus for indicating a possible compromise of the
boundary if the first verifying quantum system and the second
verifying quantum system are not likely quantum mechanically
entangled in the at least one monitored physical property.
[0005] A further embodiment provides a system for monitoring the
integrity of a communication link. The system includes a source
apparatus for generating a first and a second quantum system, where
the first and the second quantum systems are quantum mechanically
entangled in at least one monitored physical property, and where
each monitored physical property has a value pair corresponding to
the first and the second quantum system. There is a first receiver
and a second receiver that are operatively connected by the
communication link. A transmission apparatus is provided for
directing the first quantum system through the communication link
to the first receiver and for directing the second quantum system
to the second receiver. There is a first evaluation apparatus for
estimating a first value of each monitored physical property of a
first verifying quantum system received by the first receiver, and
there is a second evaluation apparatus for estimating a second
value of each monitored physical property of a second verifying
quantum system received by the second receiver. An alarm system is
provided for indicating a possible compromise of the communication
link if the estimated first value of each monitored physical
property of the first verifying quantum system and the estimated
second value of each monitored physical property of the second
verifying quantum system are not likely equal to the value of each
monitored physical property.
[0006] Another embodiment provides a system for monitoring the
integrity of a transmission of a quantum system. This embodiment
includes an apparatus for generating the quantum system with an
as-transmitted value of a monitored physical property. A
transmission medium is provided as is a receiver and a transmission
apparatus for directing the quantum system through the transmission
medium to the receiver. There is an evaluation system for
estimating an as-received value of the monitored physical property
of a verifying quantum system received by the receiver, and an
alarm system for comparing the as-transmitted value of the
monitored physical property of the transmitted quantum system with
the as-received value of the monitored physical property of the
verifying quantum system. The alarm system indicates a possible
compromise of the transmission of the quantum system if the
estimated as-received value of the monitored physical property of
the verifying quantum system does not likely correspond to the
as-transmitted value of the monitored physical property of the
transmitted quantum system.
[0007] A method is provided for monitoring the integrity of a
boundary. The method includes a step of generating a first and a
second quantum system, where the first and the second quantum
systems are quantum mechanically entangled in at least one
monitored physical property. A further step includes transmitting
the first quantum system through a transmission medium along the
boundary to a first receiver and transmitting the second quantum
system to a second receiver. Another step is estimating whether the
first verifying quantum system received by the first receiver and
the second verifying quantum system received by the second receiver
are quantum mechanically entangled in the at least one monitored
physical property. The method also provides for generating an
indication of possible compromise of the boundary if the first
verifying quantum system and the second verifying quantum system
are not likely quantum mechanically entangled in the at least one
monitored physical property.
[0008] A further method embodiment is a method for monitoring the
integrity of a communication link. This embodiment includes a step
of generating a first and a second quantum system, where the first
and the second quantum systems are quantum mechanically entangled
in at least one monitored physical property, with each monitored
physical property having a value pair corresponding to the first
and the second quantum system. A further step is transmitting the
first quantum system through the communication link to a first
receiver and transmitting the second quantum system to a second
receiver. Two additional steps are estimating a first value of each
monitored physical property of a first verifying quantum system
received by the first receiver, and estimating a second value of
each monitored physical property of a second verifying quantum
system received by the second receiver. The method further provides
for comparing the estimated first value of each monitored physical
property of the first verifying quantum system with the estimated
second value of each monitored physical property of the second
verifying quantum system. A further step is generating an
indication of a possible compromise of the communication link if
the estimated first value of each monitored physical property of
the first verifying quantum system and the estimated second value
of each monitored physical property of the second verifying quantum
system are not likely equal to the value pair of each monitored
physical property.
[0009] A further method embodiment is provided for monitoring the
integrity of a transmission of a quantum system. This embodiment
includes the steps of generating the quantum system with an
as-transmitted value of a monitored physical property, transmitting
the quantum system through a transmission medium to a receiver, and
estimating an as-received value of the monitored physical property
of a verifying quantum system received by the receiver. A further
step is comparing the as-transmitted value of the monitored
physical property of the transmitted quantum system with the
estimated as-received value of the monitored physical property of
the verifying quantum system. Also provided in this embodiment is a
step of indicating a possible compromise of the transmission of the
quantum system if the estimated as-received value of the monitored
physical property of the verifying quantum system does not likely
correspond to the as-transmitted value of the monitored physical
property of the transmitted quantum system.
[0010] Further provided is a method for verifying the integrity of
a physical perimeter. This embodiment includes the steps of
generating an entangled pair of first and second quantum systems,
directing the first quantum system about the physical perimeter,
and comparing the first quantum system with the second quantum
system for verification of the authenticity of the first quantum
system.
BRIEF DESCRIPTION OF THE DRAWINGS
[0011] Various advantages are apparent by reference to the detailed
description in conjunction with the figures, wherein elements are
not to scale so as to more clearly show the details, wherein like
reference numbers indicate like elements throughout the several
views, and wherein:
[0012] FIG. 1 is a somewhat schematic view of a system for
monitoring the integrity of a boundary.
[0013] FIG. 2 is a somewhat schematic view of equipment for
generating and comparing quantum mechanically entangled
photons.
[0014] FIG. 3 is a somewhat schematic view of a device for
assessing polarization entanglement.
[0015] FIG. 4 is a schematic view of a quantum teleportation
intrusion schema.
[0016] FIG. 5 is a somewhat schematic view of a system for
monitoring the integrity of a communication link.
[0017] FIG. 6 is a somewhat schematic view of a system for
monitoring the integrity of a transmission of a quantum system.
[0018] FIG. 7 is a plot of visibility measurements made for both
entangled and unentangled photon pairs.
[0019] FIG. 8 is an experimentally derived receiver operating
characteristic curve for a system for monitoring the integrity of a
boundary.
[0020] FIG. 9 is a plot of detection probabilities over distance
for three attenuation factors.
DETAILED DESCRIPTION
[0021] In the following detailed description of the preferred
embodiments, reference is made to the accompanying drawings, which
form a part hereof, and within which are shown by way of
illustration the practice of specific embodiments of systems and
methods for monitoring the integrity of boundaries, communications
links and transmission of quantum systems. It is to be understood
that other embodiments may be utilized, and that structural changes
may be made and processes may vary in other embodiments.
[0022] There are many government, industrial, commercial,
institutional, and personal situations where it is desirable to
maintain the integrity of a boundary. The term "boundary" as used
herein refers to a spatial demarcation that separates a region in
which some level of protection is intended from a region in which a
lesser level or no level of protection is intended. Examples of a
boundary are a fence line of a military base, a tool crib, a school
yard, and a door of a home. The interruption of a beam of light is
commonly used to detect the passage of a person or object across a
boundary, and thereby indicate a potential compromise of the
integrity of a boundary. For example, a visible or invisible "laser
tripwire" functions by transmitting light along a boundary to a
remote receiver. When the beam of light is blocked, its absence at
the receiver signals an alarm. This sensing strategy is vulnerable,
however, to an intercept-resend attack, i.e., an attack in which an
intruder intercepts the incoming beam of light, accurately records
its properties (to arbitrary precision), and resends a perfect
duplicate to the receiver. A similar vulnerability arises with
classical electronic surveillance systems such as closed-circuit
TV, burglar alarms, and tamper-indicators. This vulnerability
arises in the context of a classical physical system because an
intruder has an opportunity to reliably intercept and measure
classical information describing the transmitted signal and to
reproduce the signal and send the reproduced signal to the
receiver, leaving a physical gap in the protection of the
boundary.
[0023] The ability to copy, or clone, information is a
vulnerability that is inherent with classical physical boundary
systems. This vulnerability, however, does not exist within the
context of quantum mechanics systems. Quantum mechanics is a set of
principles underlying the most fundamental known properties of all
physical systems. Notable among these principles are both a dual
wave-like and particle-like behavior of matter and radiation. More
specifically and pertinent to this disclosure, a generally-accepted
"no-cloning" theorem states that an arbitrary quantum of
information, e.g., an unknown qubit, cannot be reliably cloned due
to fundamental restrictions imposed on measurement by the linearity
of quantum mechanics. This characteristic provides an
entanglement-based alternative to the transmission of classical
information across a physical boundary, and depending on the
embodiment implemented, substantially all or at least a large
portion of the vulnerability to an intercept-resend attack is
negated.
[0024] FIG. 1 illustrates an example of a system 10 for monitoring
the integrity of a boundary using quantum mechanically entangled
systems. The system 10 is configured to protect a boundary 14
portion of a perimeter 18 of a physical space. In some embodiments
the system 10 may be configured to protect the entire perimeter
18.
[0025] The system 10 of FIG. 1 has a source apparatus 22 that
generates a first 26 and a second 30 quantum system. In the
embodiment of FIG. 1 the source apparatus 22 is a spontaneous
parametric down conversion (SPDC) photon pair generator, and the
first 26 and the second 30 quantum systems are quantum mechanically
entangled photons. Quantum entanglement is a possible configuration
of two quantum mechanical systems that are linked together so that
at least one physical characteristic of one system is inextricably
conditioned by a corresponding physical condition of the second
system, even though the individual systems may be spatially
separated. Ideally, when the first 26 and the second 30 quantum
systems are photons, each quantum system is a single true photon.
However, the first 26 and the second 30 quantum systems may
acceptably be approximations of a single photon (or single pair)
state.
[0026] In the embodiment of FIG. 1 the first 26 and the second 30
quantum physical systems have quantum mechanically entangled
polarizations. In other embodiments the first 26 and the second 30
quantum systems may be photons having quantum entangled
frequencies, or may be photons having both quantum entangled
polarizations and quantum entangled frequencies. In other
embodiments the first 26 and the second 30 quantum systems may be
entangled semiconductor quantum dots instead of entangled
photons.
[0027] In the embodiment of FIG. 1 there is a transmission medium
34 that is disposed adjacent the boundary 14. In the embodiment of
FIG. 1 the transmission medium 34 is a fiber optic cable and
photons are beamed through the fiber optic cable. In other
embodiments the transmission medium 34 may be the atmosphere and
photons are beamed through the atmosphere. The "atmosphere," as the
term is used here, encompasses any translucent environment
including the vacuum of outer space and the waters of the world. In
embodiments where the first quantum system 26 and the second
quantum system 30 are entangled semiconductor quantum dots the
transmission medium 34 may be an electrical conductor.
[0028] Typically the transmission medium 34 is physically
integrated with the boundary 14. For example, if the boundary 14
includes a fence, the transmission medium 34 (which in the example
of FIG. 1 is a fiber optic cable) may be woven into the fence.
Consequently a compromise of the transmission medium 34, such as a
break in the fiber optic cable, is indicative of a loss of
integrity of the boundary. If the atmosphere is the transmission
medium then the photon transmission beam passes through the
atmosphere along the border and the transmission medium is
typically breached by a blockage of the photon beam by a physical
object, which is indicative of a loss of integrity of the boundary.
The type of actions that may result in a malevolent compromise of
the transmission medium depends upon the nature of the physical
area being protected. For example if the protected area is a
military installation, the loss of integrity of the boundary may be
the result of an intrusion by an armed force. If the protected area
is a prison the loss of integrity of the boundary may be the result
of a prisoner escape. If the protected area is an information
processing system the loss of integrity of the boundary may be the
result of an attempt to electronically or visually acquire
information from the information processing system.
[0029] Returning to the details of FIG. 1, the source apparatus 22
is constructed in a cross-ringed photon emission configuration. A
transmission apparatus 38 is provided and the transmission
apparatus 38 comprises an optical coupling device that receives the
first 26 and the second 30 quantum systems from the intersections
of the crossed rings produced by the source apparatus 22. The
transmission apparatus 38 directs the first quantum system 26 in
the directions 42 and 46 through the transmission medium 34 to a
first receiver 50, and directs the second quantum system 30 through
a reliable path 54 to a second receiver 58.
[0030] Under normal operations where there has been no compromise
of the transmission medium 34, the first receiver 50 receives a
first verifying quantum system 62, which is the first quantum
system 26. However if the transmission medium 34 has been
compromised by, for example, a breach of the boundary 14 and the
transmission medium 34 at zone 66, the most likely outcome is that
the first quantum system 26 is destroyed and no first verifying
quantum system 62 arrives at the first receiver 50. This condition
is identified as a possible compromise of the boundary 14 in the
same fashion as a conventional laser tripwire system identifies
such a breach. However, if the transmission medium 34 has been
compromised by a sophisticated intercept/resend device, such as
device 70 depicted in FIG. 1, a quantum system--namely verifying
the first quantum system 62 may arrive at the first receiver
50.
[0031] Under normal circumstances at about the same time that the
first receiver 50 receives the first verifying quantum system 62,
the second receiver 58 receives a second verifying quantum system
74, which is the second quantum system 30. However, if the reliable
path 54 is compromised, either no second verifying quantum system
74 is received by the second receiver 58 or, if the reliable path
54 has been compromised by a sophisticated intercept/resend device,
a second verifying quantum system 74 may arrive at the second
receiver 58. The system 10 is capable of detecting a compromise of
either the transmission medium 34 or a compromise of the reliable
path 54, but the system 10 is not capable of detecting a
coordinated compromise of both the transmission medium 34 and the
reliable path 54 that would include essentially a substitute
system. Although such an attack is quite unlikely, the system 10 is
typically configured so that the reliable path 54 is in a secured
environment that is not vulnerable to compromise, and therefore
there is negligible chance that the second verifying quantum system
74 is not the second quantum system 30.
[0032] The system 10 also includes an evaluation apparatus 78. The
evaluation apparatus 78 assesses the first verifying quantum system
62 received by the first receiver 50 and assesses the second
verifying quantum system 74 received by the second receiver 58. The
evaluation apparatus 78 is typically a single apparatus in a single
location (and preferably a secure location) that assesses the
quantum properties of both the first verifying quantum system 62
and the second verifying quantum system 74. As previously
indicated, in the embodiment of FIG. 1 the first quantum system 26
and the second quantum system 30 have a quantum mechanically
entangled polarization property. The evaluation apparatus 78
assesses the visibility of the correlated polarization properties.
Assessing the visibility of the polarization correlations typically
requires a series of different measurements made on an ensemble of
identical biphoton states. This visibility assessment is used to
estimate whether the first verifying quantum system 62 and the
second verifying quantum system 74 are quantum mechanically
entangled in the entangled polarization property of the first
quantum system 26 and the second quantum system 30.
[0033] The system 10 of FIG. 1 further includes an alarm system 82
that is used to indicate a possible compromise of the boundary 14
if the first verifying quantum system 62 and the second verifying
quantum system 74 are not likely quantum mechanically entangled in
the entangled polarization property of the first quantum system 26
and the second quantum system 30.
[0034] FIG. 2 illustrates various elements of a quantum mechanical
entanglement system 100. The system 100 includes a source apparatus
104 for generating a "patrol" 108 and a "guard" 112 photons. The
patrol 108 photon is analogous to the first quantum system 26
described with reference to FIG. 1, and the guard 112 photon is
analogous to the second quantum system 30. The patrol photon 108
and the guard photon 112 are quantum mechanically entangled in at
least one monitored physical property. The term "monitored physical
property" indicates that the patrol 108 and the guard 112 photons
may possess a multitude of entangled physical properties, but only
one or some of them are monitored by the system 100. The source
apparatus 104 is a polarization-entangled photon-pair source based
on a type-II spontaneous parametric down conversion (SPDC) device.
A nonlinear optical crystal 116, such as .beta.-Barium Borate
(BaB.sub.2O.sub.4, often abbreviated as "BBO"), mediates the
spontaneous down conversion of a high-frequency (blue) pump photon
120 into a pair of lower frequency (red) photons, i.e., the patrol
108 and the guard 112 photons. A second, rotated BBO crystal 124
immediately follows the first crystal 116 to compensate for group
velocity differences between the down-converted photons.
Conservation of energy and momentum requires that the photons
satisfy the equations
.omega. pump = .omega. G + .omega. P and ( Eq ` n 1 ) k pump = k G
.perp. + k P .perp. ( Eq ` n 2 ) ##EQU00001##
where .omega..sub.j and k.sub.j.sup..perp.denote the longitudinal
frequency and the transverse momentum of the j.sup.th photon,
respectively.
[0035] The polarization-entangled state of a photon-pair generated
by SPDC can be approximated by the Bell state
.PHI. PG .apprxeq. 1 2 ( h P , v G + v P , h G ) ( Eq ` n 3 )
##EQU00002##
[0036] where the joint-polarization state |h.sub.P,
v.sub.G=|h.sub.P.times.|v.sub.G is the direct product of
single-photon horizontal and vertical polarization states |h and
|v, respectively, and the subscripts denote patrol (P) or guard (G)
photons. This Bell state represents one of four maximally
polarization-entangled biphoton states. The validity of this Bell
state approximation is determined by the pulse power and the
magnitude of the second-order susceptibility. Moreover, the
polarization entanglement of this state can be expressed in terms
of the experimentally measureable polarization-correlation
visibility. (There is a one-to-one correspondence between the
visibility and the von Neumann entropy of the state.) The
visibility V quantifies the fringe contrast of the
polarization-correlation spectrum obtained in either the h-v
measurement basis or the conjugate diagonal-anti-diagonal (also
referred to herein as .+-., 45/-45 and 45.degree./-45.degree.)
measurement basis. Here the diagonal (+) and anti-diagonal (-)
basis states are defined as |.+-.=(|h.+-.|v)/ 2.
[0037] FIG. 2 further depicts two receivers 128 and 132 (analogous
to the first receiver 50 and the second receiver 58 described in
conjunction with FIG. 1). Signals from the receivers 128 and 132
are received by an evaluation apparatus 136 (analogous to the
evaluation apparatus 78 of FIG. 1) through communication links 140
and 144, 148, and 152. The signals conveyed through communication
links 140, 144, 148, and 152 are electrical signals generated by
single-photon detectors (SPDs) 208A and 208B. Single-photon
detectors are not strictly required, but they are assumed herein to
simplify the analysis. The SPDs 208A and 208B may be single-photon
avalanche photodiodes that are commercially available. Each SPD
emits an electrical signal when a photon is absorbed. The specific
type of electrical signal may vary from vendor to vendor, but the
electrical signal is usually transformed to an electronic logic
signal, and electronics are provided to indicate a "coincident"
detection within a specified time window. The duration of the time
window depends upon the particular application requirements. If the
duration of the time window is too short, the verification of
reception of authentic entangled photon pairs may be missed because
the time window did not permit the "simultaneous" detection of the
paired photons. If the time window is too long a false "matching"
photon may be received and mistakenly interpreted a paired photon.
It is often beneficial to employ an electronic delay for one of the
inputs (the input that represents the photon that travels the
shortest distance to its SPD [208A or 208B]) in order to improve
the ability to detect authentic photon pairs.
[0038] As an example of a coincidence detection unit, the
evaluation apparatus 136 may include a coincidence logic unit
having two input channels and one output channel. When two logic
pulses are received as inputs within a specified time interval, the
logic unit generates a logic pulse in the output. It is typical to
monitor this collection process with a (digital) computer running
commercially available data acquisition software.
[0039] FIG. 3 depicts further details of a receiver 200. The
receiver 200 is used for sensing polarization correlation
information between the patrol 108 and guard 112 photons. In FIG. 3
a photon 204 (representative of either a patrol 108 or a guard 112
photon) arrives at the receiver 200. When each entangled photon
pair is generated each of the paired photons are entangled in all
of the polarization characteristics, e.g., (a) h/v polarization
with a value pair of [0.degree., 90.degree.], (b)
diagonal/anti-diagonal polarization with a value pair of
[+45.degree., -45.degree.], and (c) circular polarization with a
value pair of [right, left]). In the embodiment of FIGS. 2 and 3,
the selection of h/v polarization versus diagonal/anti-diagonal
polarization for monitoring is made by the angular setting of a
.lamda./2 wave plate 216 which is rotated about the transmission
axis. Assuming that the .lamda./2 wave plate 216 is set for optimal
h/v polarization detection (a setting that may be determined by
trial adjustments of the rotation angle), h-polarized photons will
pass through the .lamda./2 wave plate 216 and arrive at a
polarizing beam splitter (PBS) 212 where they continue to the SPD
208A, whereas v-polarized photons will pass through the .lamda./2
wave plate 216 and be reflected to SBP 208B. Thus, if receiver 128
of FIG. 2 receives an h-polarized photon in SPD 208A at the same
time (i.e., within the specified time window) as receiver 132
receives a v-polarized photon in its SPB 208B, it is likely that
this represents identification of an authentic pair of h/v
polarization entangled photons.
[0040] A sophisticated intruder might somehow determine that the
system 100 was monitoring h/v polarized photons, and after
compromising the transmission medium, employ an intercept-resend
device in an attempt to inject h and/or v polarized photons into
the patrol photon path. To counteract that threat it is helpful to
frequently rotate the .lamda./2 wave plate 216 90.degree.
simultaneously in both the receivers 128 and 132 so that they are
detecting a pseudo-random variation of h/v and
diagonal/anti-diagonal polarized photons. In other words, the
system may monitor coincidence rates for eight settings of the
guard (G) and patrol (P) receivers: (G0, P0), (G0, P90), (G90, P0),
(G90, P90), (G45, P45), (G45, P-45), (G-45, P45), and (G-45, P-45).
Such a monitoring pattern would be difficult for an intruder to
copy.
[0041] Also, polarization-entangled photon-pairs have the property
of correlated circular polarizations. Polarization may be
transformed from circular to linear with a quarter-wave (.lamda./4)
plate. Thus, if a receiver is oriented to distinguish 0.degree. and
90.degree. linear polarization, then the addition of a half-wave
plate converts the receiver so that it distinguishes 45.degree. and
-45.degree. linear polarization (as previously discussed), and the
addition of a quarter-wave plate converts the receiver so that it
distinguishes right and left circular polarization. It is not
necessary to install and remove the wave plates; they can all be
left in the path. One set of wave plate orientations will transform
45/-45 to h/v; another set of orientations will transform
right/left to h/v; and another set of orientations will leave the
polarization property unchanged. In fact, there are an infinite
number of polarization properties (45/-45, h/v, and right/left
being three) and for each polarization property, there exists a
combination of quarter wave plate and half wave plate orientations
that will transform that state to linear.
[0042] It should be noted that several variations of receiver and
SPD detectors may be employed. For example, a simpler (less
expensive) system may be built using only one SPD in each receiver.
That is, one receiver would have a 208A-type SPD and the other
receiver would have a 208B-type SPD. The receiver with the
208A-type SPD would not require a polarizing beam splitter (PBS)
212. Another variation is to split the incoming receiver path at
each receiver point in two directions--with one path going to an
h/v polarization detection system and the other path going to a
diagonal/anti-diagonal detection system. This configuration would
not require any mechanical rotation of a .lamda./2 wave plate.
[0043] Returning to FIG. 2, the evaluation apparatus 136
accumulates a record of the coincident counts over a series of
trials. Assuming the PBS 212 transmits horizontally polarized
photons and reflects vertically polarized photons, the conditional
probability for joint horizontal detection of the Bell state
(Equation 3) at the patrol and guard receivers is
R.sub.C(.theta..sub.P,.theta..sub.G)=sin.sup.2(.theta..sub.P+.theta..sub-
.G) (Eq'n 4)
where .theta..sub.P and .theta..sub.G are the corresponding
analyzer angles. Measurements made in the conjugate .+-. basis are
obtained by rotating the incoming photons using a .lamda./2 wave
plate. Moreover, those measurements yield a result similar to Eq.
(4) apart from a .pi./2 phase shift. Hence, for the
polarization-entangled state of Eq. (3), the empirical definition
of the visibility as the contrast
V = R C max - R C min R C max + R C min ( Eq ` n 5 )
##EQU00003##
has a maximum of unity in either basis. In contrast, an unentangled
state is predicted to have a visibility of zero in at least one
basis, independent of whether the received state is a pure state,
e.g., |h.sub.P, v.sub.G or |v.sub.P, h.sub.G, or the classical
mixture
.rho. PG = 1 2 ( h P , v G h P , v G + v P , h G v P , h G ) ( Eq `
n 6 ) ##EQU00004##
Thus, measuring the visibility provides an experimental means to
quantify polarization entanglement and, therefore, differentiate
between an ensemble of polarization-entangled states and the
unentangled states prepared by a would-be intruder. (The term
"intruder" refers to any malevolent entity attempting to defeat the
integrity of a border.) An unentangled pure state implies the
intruder chose the `correct` measurement basis, while a mixed state
implies the conjugate basis was used. For the unentangled states
above, the visibility vanishes when measured in the .+-. basis.
[0044] It is generally possible to quantify an appropriate
sensitivity and specificity for a sensor to detect entanglements
using the visibility characteristic of Equation 5 by incorporating
additive Gaussian noise into the model system and using a binary
decision evaluation that uses the measured visibility to
discriminate between entangled and unentangled quantum states.
[0045] The binary decision evaluation is a formulation of
(classical) detection theory for discriminating between two
hypotheses based on an observed signal:
H.sub.0:s.sub.i=V.sub.0+n (Eq'n 7A)
and
H.sub.1:s.sub.i=V.sub.1+n (Eq'n 7B)
[0046] In Equations 7A and 7B, si represents the i.sup.th instance
of the observed visibility and it is used to discriminate between
the two hypotheses and V.sub.0=0 and V.sub.1=1 are the visibilities
predicted for unentangled and entangled photon pairs, respectively,
and n is a zero-mean Gaussian random noise variable of variance
.sigma..sup.2. Considering M measurements, the corresponding
log-likelihood ratio test is:
i M s ~ i H 0 H 1 ln .lamda. d + d 2 ( Eq ` n 8 ) ##EQU00005##
Where {tilde over (s)}.sub.i=s.sub.i/.sigma.M.sup.1/2 is the
normalized sample data, .lamda. defines the threshold for
detection, and
d=M.sup.1/2(V.sub.1-V.sub.0)/.sigma. (Eq'n 9)
is the normalized displacement of the visibilities.
[0047] Discriminating between two known values in additive Gaussian
noise leads to well-known results for the corresponding probability
of detection Q.sub.d and false alarm probability Q.sub.0:
Q.sub.d=erfc(x.sub.1) (Eq'n 10A)
Q.sub.0=erfc(x.sub.0) (Eq'n 10B)
Here the complimentary error function is defined as
erfc ( y ) .ident. ( 2 .pi. ) - 1 / 2 .intg. y .infin. exp [ - x 2
/ 2 ] x ( Eq ` n 11 ) ##EQU00006##
and the limits for Q.sub.0 and Q.sub.d,
x.sub.0=(ln .lamda.)/d+d/2 (Eq'n 12A)
x.sub.1=(ln .lamda.)/d-d/2 (Eq'n 12B)
are expressed in terms of the threshold .lamda. and the
dimensionless displacement d. These results can be conveniently
represented by a receiver operating characteristic (ROC) curve,
which demonstrates the trade-off in detection sensitivity and
detection specificity using a parametric plot of (Q.sub.0, Q.sub.d)
with respect to the detection threshold .lamda..
[0048] Measurements of the visibility are useful for quantitatively
discriminating between entangled and unentangled photon pair
states. This detection scheme need not know a priori the types of
quantum states prepared by the intruder, i.e., the detector works
just as well for pure states as mixed states based on single-mode,
polarization-entangled photon pairs. If an intruder attempts to
measure and clone the polarization state of the patrol photon, the
destruction of entanglement leads to a noticeable change in the
measurement statistics recorded by the receivers.
[0049] A more difficult situation involves a case where the
intruder has accurate knowledge about the transmission of the
patrol photon, e.g., path, bandwidth, center frequency, timing
information, etc. and the intruder, aware that the transmitted
patrol photon is entangled with the secured guard photon, uses
quantum teleportation to transfer the entangled state of patrol
photon to a doppelganger photon.
[0050] For the case of polarization-entangled photon pairs, the
intruder may employ a pair of entangled doppelganger photons, as
shown in FIG. 4. Then, by performing a Bell-state measurement on
the patrol photon and the doppelganger photon, the intruder might
be able to prepare an entangled state between the secured guard
photon and the second, transmitted doppelganger photon. This form
of teleportation, known as entanglement swapping, might be expected
to preserve the entanglement generated by the source. However this
scenario overlooks several considerations that may be used to
undermine the viability of a quantum teleportation attack. The
foremost concern is that when the Bell-state measurement succeeds,
the guard and doppelganger photons are randomly projected into a
state chosen from the set of four orthonormal Bell states. (Aside
from its probabilistic outcome, there is no linear optical form of
the BSM that succeeds deterministically.) As each of the sampled
entangled states yields a distinct set of measurement outcomes, the
visibility derived from measurements made on a series of these
randomly prepared states would be zero.
[0051] It is possible for the intruder to locally correct the
action of Bell-state measurement; however, doing so would require
the intruder to delay the transmission of the second doppelganger
photon until after the measurement of the patrol photon had
occurred. When the patrolled perimeter is the shortest distance
between two points (a straight line), then this delay in
transmission is, in principle, always detectable by the receiver.
On the other hand, if the patrol photon takes a less direct route,
e.g., by patrolling a perimeter that turns or curves, then it is
possible for the intruder to "cut corners" and "make up" time loss
in implementing these corrective actions.
[0052] An adaptation of spectrally multimode,
polarization-entangled photon pairs may be used to reject such
measures. Briefly, the visibility of the received states before and
after quantum teleportation may be examined while using an
assumption that the intruder has applied the appropriate local
unitary operation to complete the teleportation protocol and taking
into account how polarization-correlation visibility behaves
following teleportation with respect to the characteristics of the
spectral modes and spectral entanglement.
[0053] The spectrally multimode analog of the
polarization-entangled state presented in Equation 3 is
.PHI. 23 = 1 2 .intg. .omega. .intg. .omega. ' [ f ( .omega. ,
.omega. ' ) h P ( .omega. ) , v G ( .omega. ' ) + g ( .omega. ,
.omega. ' ) v P ( .omega. ) , h G ( .omega. ' ) ] ( Eq ` n 13 )
##EQU00007##
where f(.omega.,.omega.') and g(.omega.,.omega.') are normalized
joint spectral amplitudes and
|h.sub.P(.omega.)=|h.sub.P|.omega..sub.P is a horizontally
polarized patrol photon in the spectral eigenstate having frequency
.omega., etc. These states are typical of the
polarization-entangled biphoton states prepared by SPDC when a
pulsed pump pulse initiates the down-conversion process
[0054] The specific forms of the joint spectral amplitudes in
Equation 13 are strongly dependent on the type of SPDC, as well as
the material properties of the nonlinear optical medium being used.
Furthermore, the joint spectral amplitudes need not be identical or
even individually separable with respect to frequency. The joint
spectral amplitude is, however, generally decomposable as
f ( .omega. , .omega. ' ) = n = 0 .infin. .lamda. n 1 / 2 u n (
.omega. ) v n ( .omega. ' ) ( Eq ` n 14 ) ##EQU00008##
where .lamda..sub.n is the n.sup.th Schmidt coefficient and the
Schmidt modes u.sub.n and v.sub.n form a complete biorthonormal set
for the joint spectral Hilbert space. (Normalization of
f(.omega.,.omega.) implies .SIGMA..sub.n.lamda..sub.n=1.) The joint
amplitude g(.omega., .omega.') is likewise represented by a Schmidt
decomposition. For the case that Equation 14 has more than one term
in the summation, then the joint spectral amplitude is said to be
spectrally entangled, and this spectral entanglement can be
quantified in terms of the Schmidt number K defined by
K - 1 = n = 0 .infin. .lamda. n 2 ( Eq ` n 15 ) ##EQU00009##
The Schmidt number has a minimum of K=1 (an unentangled joint
spectrum) and grows monotonically as the number of modes
increases.
[0055] Analogous to the quantification of single spectral mode
polarization entanglement, the polarization entanglement of a
spectrally multimode state may be quantified in terms of the
polarization-correlation visibility. An analysis of the
polarization-correlation experiment shows that the theoretical
maximum for the visibility is given by
V=Re.intg.d.omega..intg.d.omega.'f(.omega.,.omega.')g(.omega.,.omega.')*
(Eq'n 16)
which is unity only when the joint spectral amplitudes are
identical. Moreover, the maximal visibility is independent of the
spectral entanglement.
[0056] Continuing with the analysis of quantum teleportation of a
spectrally multimode, polarization-entangled biphoton state, assume
that two pairs of photons are each prepared in a state of the
general form of Equation 13, with the first state representing the
patrol-guard (PG) pair and the second state representing the
doppelganger (DD) pair. The patrol photon and one of the
doppelganger photons are then subjected to a polarization-based
Bell-state measurement, which is accomplished by interfering the
two photons at a 50:50 beam splitter and analyzing each output
mode, e.g., in the h-v basis. Conditioned upon the coincident
detection of two photons, the resulting reduced, polarization
density matrix of the guard and second doppelganger photons is
.rho. ~ GD = 1 2 ( h G , v D h G , v D + G h G , v D v G , h D + G
* v G , h D h D , v G + v G , h D v G , h D ) ( Eq ` n 17 )
##EQU00010##
where the off-diagonal coherence term
G=.intg.d.omega..intg.d.omega.'.intg.d.omega.''.intg.d.omega.'''f.sub.GP-
(.omega.,.omega.''')g.sub.DD(.omega.''',.omega.')*g.sub.GP(.omega.,.omega.-
'')*f.sub.DD(.omega.'',.omega.') (Eq'n 18)
represents the overlap of the spectral amplitudes. The real
component of G yields the visibility expected for the
guard-doppelganger (GD) photon pair, i.e.,
V.sub.GD=Re G (Eq'n 19)
[0057] As noted in Equation 16, the initial patrol-guard state
yields maximal visibility when the joint spectral amplitudes are
identical. Assuming this relationship for both the PG and DD pairs,
the Schmidt decomposition of Equation 14 is inserted into Equation
16 to find the resulting coherence. Simplifying the analysis to the
case that the photons produce identical marginal spectra, gives the
best possible visibility of the GD pair. Specifically, the
visibility following teleportation is inversely proportional to the
spectral entanglement carried by the joint spectral amplitude,
i.e.,
V.sub.GD.sup.max=K.sup.-1 (Eq'n 20)
[0058] In the absence of spectral entanglement,
.lamda..sub.n=.delta..sub.n0, K=1, and the visibility of the
swapped GD pair matches the unit visibility of the original pair
(cf. Equation 16). However, in the limit of strong spectral
entanglement, e.g., when .lamda..sub.n.apprxeq.1/N and
K.sup.-1.apprxeq.N (with N an effective number of spectral modes),
the visibility of the GD pair can be much less than the original,
expected visibility. Consequently, when the initial spectral
entanglement between the patrol-guard photons is high, an
intruder's attempts to use quantum teleportation can be detected
based on the decrease in the observed visibility.
[0059] This last approach to verifying the authenticity of the
polarization-entangled photon pair does not require any knowledge
about discrepancies in the time of arrival of the patrol or
doppelganger photons. Hence, even when the intruder has sufficient
time to implement teleportation, the visibility it generates will
be poor and, therefore, the intruder's presence will be
detectable.
[0060] The terms "spectrally entangled" and "frequency entangled"
are used interchangeably herein. A source apparatus for generating
a pair of frequency entangled photons may be constructed as
follows. A nonlinear optical crystal, e.g., BBO, is illuminated by
a pump laser of a given spectral profile, e.g., a monochromatic or
a broadband spectral profile. The pump laser enters the crystal at
a direction that satisfies the second-order phase matching
requirements for spontaneous parametric down conversion (the exact
angle depending on the desired crystal and degree of frequency
entanglement), whereupon passing through the crystal, photons
comprising the pump laser undergo down conversion into a pair of
lower frequency photons that serve as the outputted frequency
entangled photons. Note that the conservation of energy restricts
the frequencies of the outputted photon pair to sum to the energy
of the incident pump laser photon.
[0061] A receiver for assessing spectral (frequency) entanglement
of a photon may be constructed as follows. The frequency of each
photon in the frequency entangled photon pair is measured
individually. The individual measurements of frequency can be
accomplished, e.g., using a diffraction grating to disperse each
possible frequency toward a spatially separate photon detector. The
photon detectors may be an array of single-photon detector or the
pixels in a charged coupled device (CCD) planar array. By
monitoring which frequencies are detected in coincidence events
(when a photon is observed in each arm of the measurement
apparatus), then the correlation between frequencies may be
established. The degree of frequency entanglement may then be
assessed from these measurements, e.g., by comparing the maximal
and minimal widths of the associated two-dimensional frequency
distribution.
[0062] The use of a pair of quantum systems that have a
simultaneously entangled polarization characteristic and an
entangled frequency characteristic of a first and second quantum
system is particularly useful in thwarting a teleportation attack
on a system for detecting compromise of a quantum mechanical
transmission medium. A source for polarization and frequency
entangled photons is a broadband analog of the source for
polarization entangled photons. Whereas a "polarization entangled
source" has heretofore referred to the polarization entangled
photon pair generated in a cross ringed configuration and producing
monochromatic output, a polarization and frequency entangled source
refers to similarly produced pair of polarization entangled photons
where the photons are not monochromatic, i.e., more than one
frequency is populated. Hence, the descriptions for generating
polarization entangled photons previously described herein are
augmented slightly to note that the photons generated during SPDC
are inherently spectrally multimode and that accurate accounting of
the polarization and frequency properties identifies a pair of
photons that are entangled in polarization and frequency. The
degree to which the photons are entangled in these properties can
be assessed using the receivers described as follows. When the
photon pairs are simultaneously entangled in both polarization and
frequency, the receivers for assessing such physical properties may
be constructed in the same manner described herein for detecting
frequency entanglement, supplemented by inclusion of a polarization
analyzer (as shown in FIG. 3). Monitoring coincidence counts with
respect to both the detected frequency and the corresponding
polarization provides a methodology for assessing the entangled
physical properties. As noted before, the degree of entanglement
may be determined from these measurement results. Alternatively,
the photon pair may be entangled in both frequency and
polarization, but only one of those physical properties may be
assessed by the measurement apparatus, e.g., when the polarization
correlations are the relevant property to monitor, then frequency
measurements may be ignored.
[0063] The various techniques described heretofore for detecting an
intercept-resend attack on boundary monitoring system may be
applied in other configurations for other purposes. For example,
FIG. 5 illustrates a system 250 for monitoring the integrity of a
communication link 254. The communication link 254 is exchanging
information between a first communication system 258 and a second
communication system 262. To monitor the integrity of the
communication link 254, a source apparatus 266 is provided for
generating a first 270 and a second 274 quantum system. The first
quantum system 270 and the second quantum system 274 are quantum
mechanically entangled in at least one monitored physical property.
Each of the monitored physical properties has a value pair that
corresponds to the first 270 and the second 274 quantum system. For
example, if the first 270 and the second 274 quantum systems are
polarization-entangled photon pairs, a monitored physical property
may be their h/v polarization, in which case the value pair is
(0.degree.,90.degree.). That is, if the h/v polarization of the
first quantum system 270 is 0.degree. then the h/v polarization of
the second quantum system 274 is 90.degree.. Similarly, if the
first 270 and the second 274 quantum systems are
polarization-entangled photon pairs, a monitored physical property
may be their diagonal/anti-diagonal polarization, in which case the
value pair is (+45.degree., -45.degree.), and/or a monitored
physical property may be the circular polarization of the first 270
and the second 274 quantum system, in which case the value pair is
(right,left).
[0064] The system 250 further includes a first receiver 278 and a
second receiver 282. There is a transmission apparatus 286 that is
configured to direct the first quantum system 270 through the
communication link 254 to the first receiver 278 and configured to
direct the second quantum system 274 through a reliable path 290 to
the second receiver 282.
[0065] There is a first evaluation apparatus 294 that evaluates a
first value of each monitored physical property of a first
verifying quantum system 298 received by the first receiver 278.
There is a second evaluation apparatus 302 that evaluates a second
value of each monitored physical property of a second verifying
quantum system 306 received by the second receiver 282. Typically
the reliable path 290 is a secure link so that the second verifying
quantum system 306 is the second quantum system 274.
[0066] There is an alarm system 310 that indicates a possible
compromise of the communication link 254 if the estimated first
value of each monitored physical property of the first verifying
quantum system 298 and the estimated second value of each monitored
physical property of the second verifying quantum system 306 are
not likely equal to the paired value of each monitored physical
property. In the embodiment of FIG. 5 the alarm system 310 is in
communication with the first evaluation apparatus 294 and the
second evaluation apparatus 302 through a separate communication
channel 314. In other embodiments the alarm system 310 may be in
communication with the first evaluation apparatus 294 and the
second evaluation apparatus 302 through the communication link
254.
[0067] FIG. 6 depicts an embodiment of a system 400 for monitoring
the integrity of a transmission of a quantum system 404. In the
embodiment of FIG. 6 the quantum system 404 is a photon. The system
400 includes an apparatus 408 for generating the quantum system 404
with an as-transmitted value of a monitored physical property. In
the embodiment of FIG. 6 the apparatus 408 includes a single photon
source and a device that transforms the single photon to have a
selected as-transmitted value of the monitored physical property.
For example, the single photon source may emit polarized photons
and a half-wave plate disposed in the path of the photons may be
used to establish an as-transmitted value of 90.degree.
polarization for the emitted photons. In some embodiments the
apparatus 408 may include a source apparatus for generating a first
and a second quantum system, the first and the second quantum
systems being (for example) polarization entangled, and one of the
quantum systems is used as the quantum system 404 of FIG. 6 and the
other quantum system is discarded.
[0068] The system 400 of FIG. 6 further includes a transmission
medium 412, a receiver 416 and a transmission apparatus 420 that is
configured to direct the quantum system 404 through the
transmission medium 412 to the receiver 416. The transmission
apparatus 420 is typically an optical coupling device that provides
an interface between the apparatus 408 and the transmission medium
412. The receiver 416 is typically a receiver similar to receiver
128 or 132 depicted in FIG. 2 or receiver 200 depicted in FIG.
3.
[0069] There is an evaluation system 424 that estimates an
as-received value of the monitored physical property of a verifying
quantum system 428 received by the receiver 416. There is an alarm
system 432 that compares the as-transmitted value of the monitored
physical property of the transmitted quantum system 404 with the
as-received value of the monitored physical property of the
verifying quantum system 428, and indicates a possible compromise
of the transmission of the quantum system if the estimated
as-received value of the monitored physical property of the
verifying quantum system 428 does not likely correspond to the
as-transmitted value of the monitored physical property of the
transmitted quantum system 404. Various mechanisms may be used to
ensure that the alarm system 432 knows the as-transmitted value of
the monitored physical property of the transmitted quantum system
404. For example, the as-transmitted value of the monitored
physical property of the transmitted quantum system 404 may be
communicated over a secure communication link to the alarm system
432 by the apparatus 408 that generated the quantum system 404.
Alternately, a pattern of as-transmitted values of the monitored
physical property of a series transmitted quantum systems 404 may
be known and monitored by the alarm system 432.
[0070] The system 400 of FIG. 6 may be used in various applications
including monitoring the integrity of a boundary and monitoring the
integrity of a communication link.
EXAMPLE
[0071] A polarization-entangled "quantum fence" may be constructed
using current quantum optical technology. In particular, SPDC-based
entanglement sources are readily available for generating pulsed
polarization-entangled photon pairs at rates up to
250,000/pairs/sec/mW of pump power. In addition, measurement of the
polarization-correlation visibility in conjugate bases can be
performed using an entirely passive experimental apparatus, i.e.,
on-the-fly reconfiguration is unnecessary. Moreover, both
free-space and fiber-based sensors are candidates for such
application.
[0072] As a first demonstration of these principles, a free-space
quantum fence was constructed using a polarization-entanglement
source. The purpose of the demonstration was to "simulate" the
behavior of a quantum fence system. The experimental setup had only
one detector per receiver, so the system was simply cycled through
all of the settings to generate data for all eight pairs of
polarizations (G0, P0), (G0, P90), (G90, P0), (G90, P90), (G45,
P45), (G45, P-45), (G-45, P45), and (G-45, P-45). The data sets
consisted of lists of numbers corresponding to the number of
coincidences recorded in one-second intervals. In effect, all the
data were collected for one of the eight settings, then all of the
data for the next setting, and so on. In a real system, one would
switch between settings much more rapidly in order to make things
difficult for an intruder. To simulate the intruder, coincidences
were detected between uncorrelated photons. This was done by simply
changing the electronic delay previously-mentioned herein so that
coincidences were recorded only for photons originating from
different down-conversion events. In practice, this gives a much
lower coincidence rate, so the collection window was adjusted to
give comparable overall count rates.
[0073] In this specific demonstration, an Argon laser operating at
351.1 nm pumped a 1-mm Beta Barium Borate (BBO) crystal with the
crystal axis oriented for degenerate type-II SPDC at 702 nm.
Horizontally and vertically polarized photons were emitted into
different directions under the constraint of conservation of energy
and momentum. By adjusting the orientation of the BBO crystal, the
two emission patterns can be made to intersect. In this cross-ring
configuration, one photon was emitted into each of the two spatial
paths defined by intersecting emission cones. A second, rotated BBO
crystal immediately followed the first to compensate for group
velocity differences between the down-converted photons. Each
photon then traveled .about.60 cm to a polarization analyzer, which
consisted of rotated .lamda./2 wave plates, polarizing beam
splitters, and single-photon detectors with the measurement basis
for each analyzer station chosen by the orientation of an inserted
wave plate, cf. FIG. 2.
[0074] FIG. 7 presents a time series of visibility measurements
made in the .+-. basis for both entangled and unentangled photon
pairs. Each time-point corresponds to a 1-s collection window for
measuring the maximum and minimum coincident counts of Equation 5.
Subtraction of the relatively high dark count rate leads to some
artifacts in the data, i.e., `normal` visibilities of 1.0 and
`intrusion` visibilities less than 0.
[0075] The test monitored coincidence counts over a 1-second window
and yielded maximal count rates of 188 pairs/sec and 35 pairs/sec
in the h-v and the .+-. bases, respectively. The lower count rate
in the .+-. basis was due to the use of a single-mode fiber in
front of one SPD. The visibility was calculated by recording
coincidence counts in the orientations expected to provide maxima
and minima for both the h-v and the diagonal-anti-diagonal bases;
the average corrected visibility in each basis was 0.9755.+-.0.0169
(h-v) and 0.9139.+-.0.0834 (.+-.), respectively. Visibilities
presented in FIG. 7 were obtained by subtracting the average dark
count rate of the detector(s) from the raw count rate. While much
higher visibilities might be achievable, the present results are
entirely sufficient.
[0076] Visibility measurements for unentangled photons were also
performed. In this experiment, 1-second windows of stray photons
were collected at each detector to simulate a maximally mixed
state. A maximal rate of 7.7 pairs/sec was detected with an average
visibility -0.01.+-.0.160, which is consistent with the theoretical
prediction of zero. The small negative contribution is an artifact
of using the same analyzer orientations as in the entangled photon
case; the maximum and minimum in the polarization correlation of
the stray room light were probably at slightly different
angles.
[0077] The ability of the quantum fence to sense an intruder's
presence was tested by combining the visibilities acquired for
entangled and unentangled light into the time series shown in FIG.
7. The visibility in the diagonal-anti-diagonal basis was plotted
as a function of sample number with the first 213 points
representing entangled pairs and the last 200 points representing
unentangled light.
[0078] Taking the average visibility in the normal region as a
baseline, the dimensionless displacement d was calculated with
respect to the visibility observed in the transition or intrusion
regions. Assuming a decision based on a standard deviation of
.sigma.=0.1, the average dimensionless displacement in the
intrusion region was d.apprxeq.7.3 for a value V.sub.0=0.16 (one
.sigma. away from the mean). The corresponding receiver operating
characteristic (ROC) curve is shown in FIG. 8.
[0079] FIG. 8 depicts an experimentally derived ROC curve for the
polarization-entangled quantum fence: the probability for intrusion
detection Q.sub.d and the corresponding false alarm rate Q.sub.0
are plotted for values of the dimensionless distance d=7.3 and the
standard deviation .sigma.=0.1 assuming a single measurement M=1.
For reference, note that for [0073][0001] a threshold value of
.lamda.=1 the experiment yields Q.sub.d.apprxeq.0.9999 and
Q.sub.0.apprxeq.1.311.times.10.sup.-4.
[0080] The results obtained from the experimental setup, which
transmitted each photon 0.6 m, may be used to extrapolate the
sensor's performance across longer distances. Specifically,
atmospheric attenuation may be accounted for in the model of the
patrol photon transmitted across a distance L. (This adjustment
accounts for the reduction in count rate due to attenuation,
neglecting losses in the coincidence counts due to decoherence.) At
a wavelength of 800 nm, the effects of atmospheric attenuation can
be as low as 0.2 dB/km under best weather conditions and as high as
20 dB/km in the presence of heavy mist. (The actual test system
generated photon pairs at 702 nm, but this wavelength may be tuned
by changing the pump pulse wavelength and the properties of the
nonlinear optical crystal.)
[0081] FIG. 9 depicts the detection probability as a function of
transmission distance and atmospheric attenuation. The curves are
labeled by the value of the attenuation factor and Q.sub.d is
calculated for the fixed false alarm rate of Q.sub.0=10.sup.-3.
Assuming the measurement error scales as (count rate).sup.-1/2, the
standard deviation may be expressed in terms of the transmission
distance L and the atmospheric attenuation using the initial
condition .sigma.=0.0788 at L=0.6 m. For the case of 0.2 dB/km
loss, a high probability of detection (above 0.9999) is maintained
across 3 km. For an attenuation of 20 dB/km, the transmission range
for detection probability above 0.999 is approximately 120 m.
[0082] Results of this test demonstrate that visibility
measurements provide a viable means of authenticating the
entanglement of a photon pair. Even with a modest experimental
setup, a polarization-entangled quantum fence senses intrusions
with a high probability of detection and a low false-alarm rate
over a long range of transmission distances. A quantum fence using
brighter, pulsed sources of polarization-entangled photon pairs,
with count rates reported as high as 250,000 pairs/sec, could yield
similar performance characteristics while requiring a collection
window as short as 1 ms.
[0083] The foregoing descriptions of embodiments have been
presented for purposes of illustration and exposition. They are not
intended to be exhaustive or to limit the embodiments to the
precise forms disclosed. Obvious modifications or variations are
possible in light of the above teachings. The embodiments are
chosen and described in an effort to provide the best illustrations
of principles and practical applications, and to thereby enable one
of ordinary skill in the art to utilize the various embodiments as
described and with various modifications as are suited to the
particular use contemplated. All such modifications and variations
are within the scope of the appended claims when interpreted in
accordance with the breadth to which they are fairly, legally, and
equitably entitled.
* * * * *